A die is rolled three times. Find the probability that exactly one odd number turns up among the three outcomes.

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is 

(A) $\dfrac{1}{6}$, (B) $\dfrac{3}{8}$, (C) $\dfrac{10}{8}$, (D) $\dfrac{1}{2}$. 

(GATE 1998) 

Answer: (B) $\dfrac{3}{8}$ 

Explanation: 

Probability of getting an odd number when a die is rolled = $\dfrac{3}{6} = \dfrac{1}{2}$. 

Hence, the probability of 'success', $p = \dfrac{1}{2}$.  

No. of trials, $n = 3$. 

Therefore, the required probability is 

$= ^3C_1 \times \dfrac{1}{2} \times \left(\dfrac{1}{2}\right)^{3-1}$, from the Binomial distribution with parameters $n = 3$ and $p = \dfrac{1}{2}$ 

$= \dfrac{3}{8}$.